Just to clarify what happened here:
The raid on Cohen was not done by Mueller. Mueller’s Investigation had revealed possible criminal activity, and he referred the matter to federal prosecutors in New York. The DOJ has confirmed that Cohen has been under criminal investigation for months. The raid was performed by the FBI, executed by the US Attorney’s office in New York. The US attorney was assigned by Sessions in January, and the warrants were authorized by a federal judge.
Trump’s attorneys then filed a letter with the court that Trump should be allowed to review all material seized for attorney-client privilege.
Normal procedure is a “taint team”— lawyers not affiliated with the case— review the material for attorney-client privilege so that any material covered is never seen by those involved in the case. Trump’s request is unprecedented and illogical— it would essentially allow those under investigation to determine what material they think should be admissible. Obviously, that can’t work.
Note that attorney-client privilege doesn’t cover any old conversation that happens with an attorney. If they are not acting in the capacity of attorney, generally it does not apply. And if the conversation is about fascilitating a crime, then it also does not apply— eg Telling an attorney you robbed a bank is privileged. Discussing plans to rob a bank is not.
Because of this letter and similar arguments by Cohen’s attorneys (they want a “special master” to review the documents instead of the usual “taint team”), a judge held a hearing about it. This hearing required that Cohen’s attorneys actually reveal who his clients are. They named Trump and Broidy but refused to name the third because he was a “prominent person” who wanted to keep his identity secret. The judge overruled this, and was going to accept the name privately, but an attorney for the press successfully argued that it should be public. The third ended up being Hannity.
Hannity claims that he never retained Cohen, or paid him for legal fees, but that they had informal chats about real estate. If so, then Cohen and his attorneys must be pretty confused. Also, these chats wouldn’t be covered by attorney-client privilege.
It also leaves Hannity’s integrity on the line since he’s been strongly defending Cohen and arguing against his investigation, without providing a disclaimer that he personally knows him and has sought his legal advice, which would be standard journalistic practice.